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Approximate controllability for a linear model of fluid structure interaction

Published online by Cambridge University Press:  15 August 2002

Axel Osses  and
Jean-Pierre Puel
Axel Osses
Affiliation:
Universidad de Chile, Departamento de Ingeniería Matemática, Casilla 170/3, Correo 3, Santiago, Chile; [email protected].
Jean-Pierre Puel
Affiliation:
Université de Versailles Saint-Quentin and Centre de Ma thé ma ti ques Appliquées, École Polytechnique, 91128 Palaiseau Cedex, France; [email protected].
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Abstract

We consider a linear model of interaction between a viscous incompressible fluid and a thin elastic structure located on a part of the fluid domain boundary, the other part being rigid. After having given an existence and uniqueness result for the direct problem, we study the question of approximate controllability for this system when the control acts as a normal force applied to the structure. The case of an analytic boundary has been studied by Lions and Zuazua in [9] where, in particular, a counterexample is given when the fluid domain is a ball. We prove a result of approximate controllability in the 2d-case when the rigid and the elastic parts of the boundary make a rectangular corner and if the control acts on the whole elastic structure.

Keywords

Controllabilityfluid-structure interactionnonsmooth domainsunique continuation property.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 4 , 1999 , pp. 497 - 513
Copyright
© EDP Sciences, SMAI, 1999

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